A large wooden floor is constructed with wood-planks which are 2 inches wide. A uniform circular disk of diameter 2.25 inches is dropped at random on the floor. What is the probability that the disk touches three of the wood-planks? Give your answer as a decimal rounded to four places (i. e. X.).

Step-by-step explanation:

The side length of each wooden plank is 2 inches.

Area of each wooden plank is

Area = 2² = 4 inches²

Area of 3 wooden planks is 3 × 4 = 12 inches²

The formula for determining the area of the circular disc is expressed as

Area = πr²

π = 3.14

Radius, r = diameter/2 = 2.25/2 = 1.125 inches

Area of circular disc = 3.14 × 1.125² = 3.974

Probability is expressed as

Number of favorable outcomes/number of total outcomes

Therefore, the probability that the disk touches three of the wood-planks is

3.974/12 = 0.3312

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol